Step 1
Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal. The opening and shutting of a lunchbox, solving a Rubik's cube, and never-ending parallel railway tracks are a few everyday examples of corresponding angles. These are formed in the matching corners or corresponding corners with the transversal.
Step 2
We are given;
[tex]\begin{gathered} \angle1\cong\angle3 \\ \angle2\cong\angle5 \\ \angle3\cong\angle10 \end{gathered}[/tex]Since, we know that If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.
[tex]\angle2\cong\angle5(\text{ Alternate interior angles\rparen}[/tex]The lines in connection with this are;
[tex]\begin{gathered} Transversial\text{ is l and the two parrallel line are j and k} \\ \end{gathered}[/tex]Reason; If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.
Step 3
We are also given;
[tex]\angle1\cong\angle3(corresponding\text{ angles\rparen}[/tex]We know that If a transversal intersects two parallel lines, the corresponding
angles are congruent.
[tex]\begin{gathered} The\text{ transversal is l and the parallel lines are j and k} \\ Hence\text{ again l,j nd k are parallel} \end{gathered}[/tex]Also;
[tex]\angle3\cong\angle10(Alternate\text{ exterior angles \rparen}[/tex]We know that If a transversal intersects two parallel lines, then alternate
exterior angles are congruent.
[tex]Transversal\text{ is K and the parallel lines are l and m}[/tex]Therefore all four lines j,k,l, and, m are parallel lines. The reasons are;
1) If two alternate exterior angles are congruent then for this to be true a transversal must intersect 2 parallel lines
2) If two alternate interior angles are congruent then for this to be true a transversal must intersect two parallel lines
3) If two corresponding angles are congruent then for this to be true a transversal must intersect two parallel lines.
